Posts Tagged ‘normal distribution’

In various discussions, in particular with the PC crowd, I have found at least two recurring errors concerning groups vs. individuals that are worthy of discussion:

Firstly, a highly naive conclusion (based on a correct premise): Individual variation is often greater than group differences (correct); ergo, group differences are irrelevant (very wrong), of marginal importance (very wrong), or only discussed by those who are sexist, racist, or similar (extremely wrong—and, frankly, a misstep that I find hard to comprehend).

(In principle, all physiological and psychological characteristics and talents follow a normal-distribution in the population. If one chooses to compare [original phrasing slightly ambiguous and not translatable] based on sex, one will find that the [distributions] are often different between the sexes, but one will also find that the individual variations are greater than the variations between the sexes. In other words: it is stupid to claim that men are this and women that. Just as stupid as claiming that “men are tall and women short”. If you want to belong to the stupid flock, you can obviously continue to argument like this.)

(Note here the strawman of using an unusually strong polarization: The far more typical opinions and statements would be of the type “men are taller than women”. In more detail, the claim is not correct that all characteristics follow a normal-distribution; however, very many do follow a distribution with similar characteristics—at least close to the average.)

Now, why is this line of argumentation, at best, specious? Broadly speaking, even when individual variations are large, the group variations can have a very considerable effect on group outcomes. This applies in particular when we look at groups which are dominated by individuals who (wrt at least some characteristics) belong to the upper or lower end of the distributions. Consider professors of mathematics, convicts, Olympic athletes, … However, even in daily life, the effects can be large. I strongly recommend reading The Bell Curvew, which discusses how a great number of outcomes correlate with an implicit grouping by IQ and how groups (grouped by other criteria) with different average IQs have different outcomes. (Some of La Griffe du Lion’s writingse are also quite good—and available online.) Notably, the more equal opportunity is, the more important group characteristics become for group outcome.

An additional hitch is that not all differences are dominated by individual variation. Notably, the mere existence of special cases does not imply that individual variation is the greater factor. There are many characteristics where the difference between two groups is so large that the group difference dominates. Consider the attribute height and the groups of 5 respectively 10 y.o. children for an uncontroversial example.

Secondly, the equally naive conclusion (or evil strawman?) that those who claim that group X is Q also believe that all individual members of X are Q—or that those who claim that group X is more/less Q than group Y also believe that all individual members of X are more/less Q than all individual members of Y. There is nothing wrong with statements like “Men are taller than women.” or “Ashkenazi are intelligent.”—even if there are great individual variations: The speaker will almost certainly take the existence of exceptions for granted, assume that the reader is intelligent and informed enough to also take them for granted, and consider it a given that the statement refers to group characteristics that need not apply to any specific individual. (The rare exceptions will almost always be clear from context.)

As an aside, a principally different error with very similar consequences is to assume “all quantification” where “existence quantification” (or a middle step) was intended. During my readings of relationship forums a few years ago, e.g., I saw a great number of cases where a male poster wrote something which most likely was a “some”, on the outside a “most”, e.g. “Why do women like a-holes?”—only to be met with a barrage of “Stop generalizing! We are not all like that, you misogynist!”. The point is that an unspecified quantification is not necessarily an “all” (or even a “most”), that it is highly presumptuous to assume an “all” where it is not actually stated, and that great attention to the context must be paid before raising accusations.